The thing is, it'll take literarily 5 years to get Hextech annie as a free skin.
Reason for it is because there is a 4% chance of getting a rare gem. Also you'd need a least 10 rares gems needed for a skin. It'll take about 250 chest to do so. Usually, you can only have 48 free chest per a year. That pretty much means it'll take 5 years to get around 250 chest to actually get this skin for free. smh